After delays caused by visiting relatives, the DH added some more glue. The flute is playing beautifully now. It's in the key of D, if you go along with the fact that the lowest note is F#. It's fun to play.

The crack I mentioned above was not just along a grainline. It probably started at the longitudinal join and then went up into the grainline. For some reason, that led to two different gluing sessions.

He applied the glue, put popsicle sticks around the outside away from the glue and then put a hose clamp or two over the popsicle sticks sticks to apply pressure. Then we waited at least ten hours.

For the first minutes, the flute was so breathy, it sounded like a cross between a flute and a rainstick, but very soon that went away, and now it's playing just fine.

Thanks, tM, whoever you are.